Turning a complex surface into a volume
It's actually possible with just 4 verts. Select the corner verts.



Extrude them down with EZ.

Scale them to the same height if needed using SZ0RETURN



Turn them into a face using F.



Select everything with AA and hit F again.



The fill tool is smart enough to fill the holes separately and only generates 4 more ngons.

While my mesh was fine, you can play it safe and hit CTRLN to recalculate the normals. Make sure to give kheetor's comment an upvote.